I second the speculation that there's something wrong with your cleats. Wrong position, gunk/grit in the cleats, or maybe even the wrong shims for your particular shoes. Speedplay road cleats, IME, are a bit more finicky to install. If the cleat isn't matched to the curve of the shoe's sole (using the shims), the cleat can "twist", causing the spring to bind and making it very difficult to clip or unclip.

This link shows the shims needed. A trip to the LBS for some assistance may also be a good idea.